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Various methods of extracting circuit parameters related to radiation effects and closed-form design equations based on them are provided for a one-dimensional (1D) resonant right-/left-handed transmission line (RLH-TL) with open and short terminations. The radiation properties of the RLH-TL have been characterised by simple parameters such as series resistance and shunt conductance in a unit cell using transmission line theory. In order to demonstrate the effectiveness of the modelling and to validate the design equations, two types of zeroth-order antennas based on low- and high-radiation structures have been designed, fabricated and measured. The low-radiation zeroth-order resonant (ZOR) antenna structure at 2 GHz is shown to have a very compact size (0.05λ0×0.1λ0×0.01λ0) with a limited bandwidth, whereas the high-radiation ZOR antenna structure at 10 GHz is shown to have a much wider bandwidth of about 25 , as compared with any reported ZOR antennas in currently available research publications. The modelling of the 1D resonant RLH-TL, in consideration of the radiation effects, considerably narrowed the gap between the RLH-TL characteristics based on circuit simulations and those based on electromagnetic simulations and measurements.